Abstract
Morphisms of functors or natural transformations between functors of different variance are investigated. In order to be able to define the usual compositions of morphisms of functors in this case, too, and to formulate the corresponding results smoothly, one is forced to define a morphism of functors essentially as a mapping from one category to another and not as usual as a mapping from the class of objects of one category to another category. Two new invariants of a morphism of functors, the parity and the exponent, arise in a natural way and are the main tools in proving all the results.
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